The landscape along your direct route from Austria to Black Forest isn't too interesting. But if you don't mind a detour and some winding roads then I suggest the following route wich is scenic and varied:
Day 1: First drive through Appenzell area, which is very nice - unspoilt, with soft rolling green hills and some higher mountains, beautiful villages and a rich cultural heritage. Your route could lead you through Heiden, Trogen, Teufen, Waldstatt and St. Peterszell to Wattwil. Then go southwards to Glarus. Landscape changes here and becomes dramatic with high rising mountains, partly snow topped. Drive over Klausenpass, one of the 'real' mountain passes. Descend to Lake of Lucerne and stay for the night in one of the charming villages along the shore, for instance Brunnen.
Day 2: If you like to do a mountain excursion then take the rack railway from Vitznau to Rigi (it's car free) - enjoy the view from there or do a short hike. If you prefer to visit a museum then go to Lucerne and spend some time in the very interesting transport museum. Lucerne is somewhat a hassle with a car, but the museum is outside of the city centre and there is plenty of parking. Then continue to Black Forest on direct way.